Question

[nguyễn văn tâm]

Cho A=$\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{9999}{10000}$34 .89 .1516 ...999910000 

Tính 200.A

Answer 1

[Akai Haruma]

Lời giải:
$A=\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}....\frac{99.101}{100^2}$

$=\frac{(1.3)(2.4)(3.5)....(99.101)}{2^2.3^2.4^2...100^2}$

$=\frac{(1.2.3...99)(3.4.5...101)}{(2.3.4...100)(2.3.4...100)}$

$=\frac{1.2.3...99}{2.3.4...100}.\frac{3.4.5....101}{2.3.4...100}$

$=100.\frac{101}{2}=\frac{10100}{2}=5050$

$\Rightarrow 200A=200.5050=1010000$